Peña Nieto said his government remains committed to fighting organized crime, but that the United States and Mexico must "cooperate on the basis of mutual respect, to be more efficient in our security strategy that we are implementing in Mexico."

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Obama faces reality in Mexico drug war

Obama stressed that the countries will continue to cooperate closely on security, but he didn't specify how.

"I agreed to continue our close cooperation on security, even as that nature of that close cooperation will evolve," he said.

It's up to the Mexican people, Obama said, "to determine their security structures and how it engages with other nations, including the United States."

In the meantime, he said, the United States remains committed to reducing the demand for drugs north of the border, and the southward flow of illegal guns and cash that help fuel violence.

"I think it's natural that a new administration here in Mexico is looking carefully at how it's going to approach what is obviously a serious problem," Obama said, "and we are very much looking forward to cooperating in any ways that we can to battle organized crime."

Before Obama's arrival, a spate of news reports this week on both sides of the border detailed changes in how Mexico cooperates with the United States.

Under the new rules, all U.S. requests for collaboration with Mexican agencies will flow through a single office, Interior Minister Miguel Angel Osorio Chong told Mexico's state-run Notimex news agency.

It is a drastic change from recent years, when U.S. agents enjoyed widespread access to their Mexican counterparts.

Speaking to reporters after his meeting with Obama on Thursday, Peña Nieto emphasized the importance of reducing violence, and also the importance of Mexico's relationship with the United States extending beyond the drug war.

"We don't want to make this relationship targeted on one single issue," he said. "We want to place particular emphasis on the potential in the economic relationship between Mexico and the United States."

To achieve that goal, Peña Nieto said, the presidents agreed to create a new high-level group to discuss economic and trade relations between the two nations. The group, which will include Cabinet ministers from both countries and U.S. Vice President Joe Biden, will have its first meeting this fall, Peña Nieto said.

Imports and exports between the United States and Mexico totaled nearly $500 billion last year, and before Obama's arrival officials on both sides of the border said economic relations would be a focal point during the U.S. president's visit.

"When the economy in Mexico has grown, and people have opportunity, a lot of our problems are solved, or we have the resources to solve them," Obama said Thursday.

The emphasis on the economy Thursday was a significant shift, said Jason Marczak, director of policy at the Americas Society and Council of the Americas.

"The conversations between Mexico and the United States are changing," he told CNN en Español.

Obama is scheduled to deliver a speech at the National Anthropology Museum in Mexico City on Friday morning. In the afternoon, he will travel to Costa Rica, where he will meet President Laura Chinchilla and other regional leaders.